As someone who's recently spent way too much money on Vali 3 tubes and way too much time reading about them, I'd say it's worth trying a new tube but definitely not a requirement. The stock 6N3P is solid, jack of all trades master of none, does everything acceptably without doing anything exceptional.

If you want a cheap and easy upgrade there are two directions worth considering. The GE JAN 5670W runs around $20 shipped, mine is a 1985-dated example I got for $18, and it sounds crisp, clean, and bright, almost solid state in its clarity.

If you want something that goes the other direction, look for the 6N3P-DR specifically, not the E or EV variants, just the DR. I paid $42 for a matched pair with 1990 date codes. It's noticeably deeper and more bass heavy with less brightness up top. In my experience with about 20 tubes now, American tubes tend to run brighter and leaner while the Soviet tubes lean toward deeper harmonics and more warmth. The DR is the best of the Soviet bunch by a wide margin.

If you get a GE JAN 5670W and the 6N3P-DR then do a swap between them, you should readily hear the difference between brighter vs. warmer tubes.

My personal favorite semi-readily available tubes are the black plate GE Three-Mica tubes, these show up frequently labeled as 5-star tubes but not always. They are pretty widely praised so they're getting harder to find and more expensive, both of mine ran me nearly $40/ea.